If the price of onions is raised by 30%. How much % must a household reduce its consumption, to keep the expenses constant?23.07%27%63.07%3.07

1. Break Down the Problem

We need to determine the percentage reduction in the quantity of onions that a household must make to maintain constant expenses after a 30% increase in the price of onions.

2. Relevant Concepts

Let:

• $P$ = original price of onions
• $C$ = original consumption (quantity)
• The new price after the increase = $P_{new} = P + 0.30P = 1.30P$
• Let $C_{new}$ be the new consumption quantity.

To maintain constant expenses: $\text{Original Expense} = \text{New Expense}$ $P \times C = P_{new} \times C_{new}$ This simplifies to: $P \times C = 1.30P \times C_{new}$ Dividing both sides by $P$: $C = 1.30 \times C_{new}$ Thus: $C_{new} = \frac{C}{1.30}$

3. Analysis and Detail

Next, we calculate the percentage reduction in consumption:

• The reduction in consumption $= C - C_{new} = C - \frac{C}{1.30}$
• Simplifying this gives: $C - C_{new} = C - \frac{C}{1.30} = C \left(1 - \frac{1}{1.30}\right) = C \left(1 - \frac{1}{1.30}\right) = C \left(\frac{1.30 - 1}{1.30}\right) = C \left(\frac{0.30}{1.30}\right) = C \left(\frac{3}{13}\right)$ Calculating the percentage reduction: $\text{Percentage Reduction} = \frac{C \left(\frac{3}{13}\right)}{C} \times 100 = \frac{3}{13} \times 100 \approx 23.08\%$

4. Verify and Summarize

The percentage reduction in consumption required to keep expenses constant after a 30% increase in the price of onions is approximately 23.08%.

Final Answer

23.07%